Question

see the attachment for question...
2).the acceleration of block B = ?
3).The tension in the string connecting A and B = ?

Answer 1

Let us assume that A goes down with an acceleration a1 and block B down with an acceleration a2.   Let us say the block C moves with an acceleration a3 upwards.  The equations of motion for them are:

   3 g - T = 3 a1     =>   T = 3 g - 3 a1       ---   eq 1
  5 g - T = 5 a2      =>   T = 5 g - 5 a2           --    eq 2
  2 T - 6 g = 6 a3     =>  2 T = 6 g + 3 (a1+a2)    --     eq 3 

    a3 = (a1+a3)/2  as block C moves up (x1+x2)/2 distance when A moves down by x1 and B moves down by X2 distance.
   
   Solving the above three equations,    eq 1 + eq 2 = eq 3 
    2T = 3 g - 3 a1 + 5 g - 5 a2 = 6 g + 3 a1 + 3 a2    =>   2 g = 6 a1 + 8 a2
       3 a1 + 4 a2 = g      -- eq 4
   
   eq1 = eq 2  =>   3 g - 3 a1  = 5 g - 5 a2     =>    5a2 - 3a1 = 2g   -- eq 5
    
   add eq 4 and eq   5    =>    9 a2 = 3 g    =>   a2 = g/3 

    a1 = [ g - 4 g / 3 ] /3  = -g/9
    a3 = (a1+a2)/2 = g/9     T = 3g - 3a1 = 10g/3

Block A upwards  with g/9 ,    B downwards with  g/3,  C upwards with g/9
Tension all along the string is same = 10 g/3